Rigid motions and generalized Newtonian gravitation

In an effort to contribute to a better understanding of General Relativity, here we lay the foundations of generalized Newtonian gravity, which unifies inertial forces and gravitational fields. We also formulate a kind of equivalence principle for this generalized Newtonian theory. Finally, we prove that the theory we propose here can be obtained as the non-relativistic limit of General Relativity.